Why does lower focal length magnifies objects better comparing to other camera? [duplicate]

Question

I have a newbie question about focal length, what it actually means for lenses and how I can translate this into "how close to the target it's going to practically take me" (I don't want to use the term zoom here to avoid confusion, perhaps magnifying power is what describes best what I'm after, basically shots from the distance, not macro).

Here's an example:
I currently have a Sigma 18-200mm lens (therefore approx. 11x zoom), which I use with Canon EOS 400D and also a compact Sony Cyber-Shot DSC-HX60 with focal length 4.3-129mm (approx. 30x zoom).
Even though 200mm is obviously more than 129mm the Sony camera takes me closer to the target.
Looking at zoom factor (30x comparing to 11x) this may seem obvious, but it's less obvious when you compare it to other lenses, e.g. 200-500mm lens, which effectively has "only" 2.5x zoom, but actually takes me closer to the target.

How can I make sense of this when looking at other lenses?
For example let's consider Tamron 16-300mm, its zoom is obviously approx. 20x, but how can I compare it to Sigma 18-200mm or Cyber-Shot 4.3-129mm? Is it going to take me closer to the target, e.g. magnify objects better then both of them or only better than Sigma, but still not as good as Sony? (ignoring quality of picture of course)

Answer 1

Sony Cyber-Shot DSC-HX60 has a small sensor (6.16x4.62 mm). When talking about "Sigma 18-200mm lens", you don't mention which camera you use it on, but I guess it's an APS-C sensor (24×16 mm), hence 3.8 times bigger. At constant image size on the sensor, the small sensor will only get a tiny portion of the image, hence the subject will appear 3.8 times bigger on your Sony than with your Sigma lens mounted on an APS-C body for the same focal length.

When comparing focal length with different sensor size, it's better to compare in terms of "35mm equivalent", i.e. multiply by 1.5 for APS-C sensors, and by 5.8 for your Sony camera.

Answer 2

Your question cannot be answered that way. There are instead other factors.

Your 18-200 Sigma lens is for a APS size camera, with a relatively large digital sensor. Your little compact has a very tiny sensor (all compacts and phones do). These are very important differences regarding the size image they can show.

So to take a "reasonable" picture, showing a "normal" scene width view comparable to what all other cameras normally show, the large sensor can use a longer lens, and the tiny compact sensor must use a vastly shorter lens, very short ... in order to fit all of the normal scene onto the sensor. A much shorter lens than would be usable on the larger camera. In this way, then either camera takes a "normal" picture, showing about the same normal view, regardless that the tiny sensor is so small.

What effects how "close up" the picture can be are two things. Minimum focus distance (about 15 inches for the APS Sigma lens, and perhaps 1/2 inch for most tiny compacts). The closer it focuses, the larger the subject appears.

Also the focal length is a magnification factor, longer focal length (like telephoto) brings the subject up much closer.

And then FWIW, the larger sensors allow more enlargement of the picture.

Sigma calls it "macro", because it does focus a little closer than most normal lens, and can do a 1:3 reproduction ratio. But it is NOT a real macro lens that can to 1:1.

Here's the deal: If you want macro benefits, then you should buy a real macro lens for the APS size camera. That this what they do, focus up extremely close (a very few inches), and are optimized for the closer distances. Typically, they can do 1:1 reproduction, 1:1 meaning that the image on the sensor is the SAME size as the actual object (the APS sensor is less than 5/8 inch tall). Meaning, an image of US dime coin will be slightly larger than the APS sensor can fully show.

Then the larger sensor APS sensor size can enlarge the dickens out of it too.

Answer 3

There are several characteristics of an objective which define the sizes of objects:

• the equivalent focal length is the focal length of an objective which yields the same FoV on the 35mm film frame;
• the Field of View (FoV) defines the sizes of object on the recorded image, it is calculated from sensor dimensions and focal length and is defined as the angle between things appearing at opposite corners. The smaller the FoV is the bigger the objects appear. The formulae iswhere d is diagonal and f is focal length (in same units, be it meters or millimetres). Alternatively, use d=43 mm (the diagonal of the 35mm frame) and the equivalent focal length frequently mentioned somewhere.
• the magnification is commonly used as the biggest achievable magnification at all focal lengths and distances from sensor to the object, it is not directly derived from other characteristics. It may be achieved at both short end and long end of an objective;
• the zoom is the ratio between the smallest FoV and the biggest FoV, the smallest focal length and biggest focal length;
• crop factor is the characteristic of a sensor derived from it's size. It is the ratio between the equivalent focal length and the focal length, the ratio between 35mm film frame diagonal and the diagonal of the sensor.

For example, a 43mm objective used on the 35mm film frame (36x24mm, crop factor 1) will have 60 degree FoV and will have some 1:5 magnification when focused closely (it depends). A camera with 10,75 mm objective and 9x6mm sensor (4x crop) will have the same FoV i.e. the distant objects will occupy the same part of the frame.

You should find the size of the sensor which your camera has to compare the scale of the objects which the combination will yield.

Answer 4

Overall the image from the smaller sensor is being enlarged about 3.6X more than the image captured by the larger APS-C sensor when viewed at the same display size. That's why objects in the picture taken by the compact camera from the same distance appear larger than the same objects in the picture taken by the camera with the larger sensor.

All of the other answers dance around it, but the main reason a 129mm lens on the compact with a very small sensor makes a distant object look larger than a 200mm lens on an APS-C camera is that an image from the smaller sensor is magnified/enlarged by a much greater factor to be displayed at the same size for viewing as an image from the APS-C camera with a much larger sensor.

The APS-C EOS 400D camera has a sensor size of roughly 22x15 mm for a crop factor of 1.6X. Crop factor is based on the length of the diagonal of a sensor compared to a 36x24mm frame of film. In order to view an image at a size of 200x300 mm (≈8x12 inches) the image as it is projected onto the EOS 400D's APS-C sensor must be enlarged by a factor of about 13.5X

The Sony has a sensor that is only about 6x4.5 mm with a crop factor of 5.6X. In order to view an image at a size of 225x300 mm (≈9x12 inches) the image as it is projected onto the sensor must be enlarged by a factor of about 48.7X

Notice that the aspect ratio of the smaller sensor is 4:3 while the aspect ratio of the larger sensor is 3:2. That is, the smaller sensor is 1.333333 times wider than it is tall while the APS-C sensor is 1.5 times wider than it is tall. Our comparison here preserves the length of the long edge rather than the length of the diagonal which is why the enlargement ratios vary a bit from the relationship between each camera's crop factor.

The diagonal of a 36x24mm "full frame" is 43.27mm.
The diagonal of the APS-C sensor in the EOS 400D is 26.68mm.
The diagonal of the Sony Cyber-Shot DSC-HX60 sensor is 7.70mm.
The diagonal of a standard 8x10 print is 325.279mm (12.8 inches)